let half the circumference be multiplied into half the diameter and the product shall be the space demanded According to the second Proposition it is better to find out first the half diameter or half circumference by the foregoing Probleme although it may be dispatched without it Twelfthly The half Diameter or Diameter of any Globe being given to find the Superficies thereof in square measure The Globe called a round solid body and its solidity in Cubick measure The Globe is called a round or solid Body in whose middle there is some point out of which all the strait Lines drawn to the Superficies are equal And this point in the middle is called the center of the Globe The Line through the center is called the diameter and it is called the axis if the Globe be turned or rolled about that diameter Moreover if the Globe be cut any way howsoever the Section is the circle And if it be cut through the center or we imagine it to be drawn through the Plain the Section shall be the circle whose diameter is the same as the diameter of the Globe it self And such circles are called the greater circles of the Sphere or Globe the rest are called the lesser circles of the Sphere Therefore for the resolution of the Probleme first let the circumference of the circle be found out by the given diameter Then let the diameter be multiplied into this circumference and then the superficies of the Globe shall be the product in square Measure See Scheme Furthermore let this superficies be multiplied by the sixth part of the Diameâ—â—r and the product shall be the solidity of the Globe in Cubick Measure A Triangle Thirteenthly A Triangle is called rectangled one side of which standeth perpendicularly upon the other side or with it maketh a strait Angle of ninety degrees These two sides are called Catheti the third side is called Hypotenusa The measure of the Angles â—n the Arch. The Measure of the Angles is the Arch which is described a center being taken in the top of that Angle to wit of how many degrees that Arch intercepted between the shanks of the Angle is of so many degrees that Angle is said to be So a strait Angle is said to be ninety degrees because the Arch so described is always the Quadrant or fourth part of the circumference of the circle The Sine of an Arch. The Sine of any Arch is called a strait Line which is drawn perpendicular from the extream of the Arch into the diameter drawn through the other extream of the Arch. A Tangent of the Arch. A Tangent of that Arch is said to be a strait Line touching the Arch in one end and a strait ended Line which is drawn from the center through the other end of the Arch. But this Line thus drawn is said to be the secant of that Arch. But the Sine of an Angle is said to be the Sine of that Arch which measureth that Angle so the Tangent of the Angle and its Secant Furthermore it is to be known that by the labour and study of Mathematicians Tables were made Tables called the Mathematical Canon or Rule in which the half diameter of 100000 or of more Cyphers being taken the Sines and Tangents and Secants of all the Arches of the circumference are found out For example sake 2 degrees 10 degrees 20 degrees 32 minutes c. And these Tables are called the Mathematical Canon or Rule and have infinite Commodities in all the Mathematical and Natural Sciences And therefore I am willing to teach the Studious of Geography these few things But the principal use thereof is in the measuring as well of Spherical as plain Angles But because the measuring of Spherick Angles hath some difficulty which seemeth necessary only for them who desire to enter themselves more profoundly into Art therefore we will speak only of Triangles strait angled whose dimension any one may easily apprehend Two Theorems whose use is frequent in Geography Rules to be observed Fourteenthly Three Angles of what Triangle soever being taken together are equal to two strait Angles or are 180 degrees and therefore two Acute in a Triangle strait angled makes 90 degrees Furthermore if a strait Line touch a circular Line and from the point of their contact or meeting a strait Line be drawn to the center of the Circle this makes a strait Angle with the Line Tangent Fifteenthly But these are the Problems whose use is frequent First the Hypotenusa and together the Cathetus of a Triangle strait angled being given to find out the Angle contained or another Acute For the finding out of which let it be wrought according to the Golden Rule as the given Hypotenusa is to be the given Cathetus so the whole Sine 100000 which number is the half Diameter taken in the Tables of Sines is to the Sine of the other Angle This Sine sought out in the Canon will shew the Arch or quantity of the Angle which joyneth to the Hypotenusa But the contained Angle is the complement of the found out Angle to 90 degrees Therefore if the found out number be subtracted from 90 degrees the demanded Angle is left remaining Secondly A Cathetus and an acute adjacent Angle being given to find out the Hypotenusa Let this be wrought according to the Golden Rule as the Sine of the complement of the given Angle is to 100000 or to 1000000 in the greater Canon so is the given Cathetus to the demanded Hypotenusa Thirdly Two Cathetuses being given to find the Angle adjacent to either of them Work thus as one Cathetus is to another so is the whole Sine 100000 to the Tangent of the Angle which is adjacent to the first assumed Cathetus Fourthly A Hypotenusa and one acute Angle being given to find either Cathetus Let the Work proceed thus as the whole Sine 100000 is to the Sine of an Angle which is opposite to the Cathetus demanded so the given Hypotenusa is to that Cathetus Measures useful in Geography Because the use of Measures is very frequent in Geography and that also divers People use sundry Measures therefore I shall give the Reader some Advertisements therein The Foot the most famous Measure first found out by Snellius The famous Measure is the length of a Foot but this is very different The Rhindlandish Foot of Snellius is the now usual Mathematicians Foot which is equal to the Old Roman Foot And because Snellius was most diligent and curioâ—est in measuring the Earth therefore that Rhindlandish foot is deservedly taken for the rule of all Measures A Rod or Perch The Decempeda or Land measuring Rod containeth ten foot Rhinlandish It is also called a Peroh or Pole but Geodesians or Surveyors make a Rhindlandish Perch to be twelve Rhindlandish foot or else sixteen foot Germish or or sixteen foot and an half English The
in E B which sheweth the 52 deg of the Arch B C shall be the projecture of the Arctick Pole Let the point in E D be noted with the letter P which representeth the 52 deg of the Arch D C by accounting from C to D shall be the projecture of the intersection of the Aequator and the Meridian of London Let the letter Q be noted and from that towards the letter P let the numbers of the degrees 1 2 3 c. be ascribed Also from Q towards D and from B towards P viz. 52 53 54 55 c. Then the points being taken from P of the equal degrees viz. 99 and 99 also 88 and 88 let these be described about these parts as the Diameters of the Peripheries of the Circles which shall represent the Parallels or Circles of Latitude and the Tropicks and Polary Circles with the Aequator For the describing the Meridians To describe the Meridians first let a Periphery be described through the points A P C that shall shew the Meridian which is 90 degrees absent from London His Center shall be M in B D protracted into the point N which sheweth the Antarctick Pole Let P N the Diameter be drawn through M Parallel to A C which is F H protracted from both parts in K L. Moreover let the Circle P H N F be divided into 360 deg and Right lines from the point P to every deg or only by application of the Rule which shall cut the line K F H L. The Circles must be described through every point of the Section and both the Poles P N as through three given points which shall represent all the Meridians the Centers of the Arches to be described are seated in the same K L viz. those which are found by the former Section but to be taken with this condition that the most remote Center at L be chosen for the nearest Meridian from B D N towards A and for the second the second from this The Circles of the Latitudes and the Meridians being thus described it is easy to inscribe the places of the Earth on a Map and the scituation of them all to London will be conspicuous Moreover to affix the Rule to the place of London the same parts should be brought in into which E B was divided and the number of degrees must be ascribed so the Rule being brought round unto every place we shall presently know both how great an interval they lie from Amsterdam and in what quater they lie in respect of it Now how by the benefit of the Globe such a Map should be made we shall shew in the Fourth Mode of particular Maps The first Mode of Geographical particular Maps We have spoken of the making of general or universal Maps now it is required that we should teach the composition of particular or special Maps Of particular or special Maps as of Asia Africa Europe America The parts therefore of the Earth which we would represent on the Map are either great or small It great as Asia Africa Europe America it will be necessary to institute a Declination according to the Modes explained for General Maps but in divers parts sundey ways are more commodious Africa and America because the Aequator passeth through them are not commodiously exhibited by the first Mode but most aptly by the second the Eye being placed in the Plain of the Aequator above the middle Meridian between the extreams which shut up Africa or America Therefore in these Maps the Aequator is a right line but the Parallels and the Meridians are the Arches of the Circles But to represent Asia and Europe the first and sixth Mode are more commodious but for the Polary Lands or Frigid Zones we have said that the first Mode is most apt in the explication of the same First therefore a streight line must be drawn upon the Plain for the Meridian of the place unto which we would have the Eye hang over and that must be divided into degrees according to the Method explained in the preceeding Modes and which shall be degrees of Latitude the number of which must be ascribed Then from the Table must be extracted the Latitude of both Parallels viz. that which terminateth the Region from both sides which representeth the Poles The degrees of the Latitude of these must be noted in the right line or the Meridian of the Eye and through those points streight perpendicular lines must be drawn which inclose the Map towards the Northern and Southern quarter Then Parallels and Meridians must be drawn at every degree and the places inscribed until the Map be perfected The second Mode of describing particular Maps The second Mode of particular Maps Artificers are wont to use another Method in Regions not so large but only moderate or small First a tranverse line is drawn in the extremity of the Table for the Circle of Latitude in which the ends of the Regions respecting the Aequator are to be drawn in that so many parts are taken equally through how many deg of Longitude that Region is extended from that part Then from the middle of this line a perpendicular is drawn which hath so many parts as there are deg of Longitude between the bounds of that Region towards the Aequator and the Pole But how great these parts should be is known from the proportion of the deg of the first Circle which is greatest to the deg of Parallel which is represented from the lower transverse line Through the term of this perpendicular another perpendicular or Parallel to the inferiour line is drawn in which so many deg of Longitude must be taken as are in the lower line and equal to them of the lower line if these Latitudes be not much distant from the Aequator or mutual from themselves But if the distance from the Aequator be great or if the excess of the ultimate Latitude of the Region be great above that which is more near the Aequator the parts to be taken in the transverse line shall not be equal to the parts of the inferiour line but they ought to be lesser according to proportion which the degrees of this more remote Parallel hath to the degrees of the inferiour line which proportion is known from the Table we have placed in the Fourth Chapter See Chap. IV. After the parts are thus taken for the deg of Longitude in the superiour and inferiour line the right lines are to be drawn through the beginning and end of the parts of the same number which right lines shall represent the Meridian lines Then through every deg of its perpendicular which we have ordered to be erected from the middle point of the inferiour line lines Parallel to that lower line must be drawn through the beginnings of every degree which shall shew the Parallels of Latitude In the last place places must be inscribed at the points in which the Parallels of every
Arches of fifteen degrees beneath the Horizontal line must be taken in the described Periphery for the hours before six in the Morning and six in the Evening and the Lines of the shadows must be drawn the perpendicular Style must also be erected from the Center Furthermore In the Horizontal plain if that the Plain of the Scioterick be not yet erected the Meridian line must be found and the Line of the Aequinoctial rising and setting and so it must be placed on or above this Plain of the Scioterick that the Horizontal line of the Scioterick may be parallel to this Line of the rising and setting so the shadow of the Style shall shew the beginning of the hours at every day of the year But because the Sun only illustrateth this one Superficies of this Plain half a year and the other another half year therefore in both the Superficies a Scioterick must be made after the appointed Mode laid down before that on one side of it in the time of Summer and Spring in the other in the time of Autumn the hours may be known by the benefit of the Shadows The Lines of the Circle which shew the place of the Sun in the Ecliptick or the entrance of the Sun into the twelve Signs of the Zodiack and which do represent the Parallels which the Sun describeth in the Heaven by his circumvolution may easily be drawn on this Aequinoctial Scioterick For let a certain Magnitude of the Style be taken and let it be accurately divided into Ten parts and one of thsee Ten into ten other parts that the whole Line may be conceived to be cut into an hundred particles then from a Table of Declinations let the Declinations of the Sun be excepted the fifth the tenth the fifteenth the twentieth the twenty fifth the thirtieth degrees of Aries or the first the fifteenth degrees of Taurus the first the fifteenth degrees of Taurus the first the fifteenth degrees of Gemini the first degree of Cancer and let the Tangents be taken from the Mathematical Canon Moreover from the Center of the Horologe in the interval of the Tangent of Complement of the fifth degree of Aries let the Periphery of the Circle be described this will note the entrance of the Sun into the fifth degree of Aries and the twenty fifth of Virgo and the Parallel of the Sun for that day viz. when the diurnal extremity of the shadow by its circumvolution shall fall on this described Periphery it shall be a sign that the Sun is in the fifth degree of Aries or the twenty fifth of Virgo After the same Mode let the Peripheries be described in the interval of the Complement of the tenth and the twentieth degrees of Aries the first and the fifteenth of Taurus the first and the fifteenth of Gemini and the first degree of Cancer those will shew the Parallels of the Sun in those points and also in the points of the 20th degree of Virgo the 10th and the first of Virgo the 15th of Leo and the first of Leo and the 15th degree of Cancer After the same Mode on the other side of the Scioterick let the Peripheries be described for the Parallels of the Sun in the first degree of Libra and the 25th of Pisces in the 10th of Libra and the 20th of Pisces in the 15th of Libra and the 15th of Pisces in the first of Scorpio and the first of Pisces in the 15th of Scorpio and the 15th of Aquarius and in the first degree of Sagittarius and the first of Aquarius Unto every one of these Peripheries the Characters of the Signs of the Zodiack must be ascribed Proposition XXII To describe an Horizontal Scioterick or an Horizontal Plain An Horizontal Scioterick or Horizontal Plain described By the Globe Let the Pole and Meridian be elevated for the Latitude of the place which Meridian is more conspicuous than the other lines in the Superficies both for colour and magnitude let it be brought under the Brazen Meridian let the Index be placed at the hour of twelve let the Globe be turned round until the Index shew the hour One or Eleven or until 15 degrees of the Aequator do pass the Brazen Meridian In this scituation of the Globe let the degrees intercepted between the Brazen Meridian and the Meridian of the Globe be numbred on the Wooden Horizon and let this hour be noted for the hour of One after noon and Eleven before noon Then let the Globe be turned again until the Index shew the hour 11 or 10 and let the degree intercepted between those two Meridians the Brazen one and that assumed be noted for the 10th or 11th hour After the same manner let it be done for the hours 9 and 3 for 8 and 4 for 7 and 5 for 6 and 6 but we shall not want this hour for 5 and 7 for 4 and 8 for 3 and 9. These degrees being thus noted for every ascribed hour let the Meridian line be found on the Horizontal Plain and for any point of this line let the periphery of the Circle be described as from a Center and let it be drawn perpendicularly from the Center to the same on either side This shall be the line of the shadow at the hour 6 before noon and 6 after noon The Meridian line is the line of the shadow of the hour 12. In the described periphery let the Arches before noted be cut of beginning from the Meridian line towards the line of the hour 6 before and after noon First the Arch noted for 11 and 1 then for the hour 10 and 2 for 9 and 3 for 8 and 4 c. The Arches thus cut off let the lines be drawn from the Center to those bounds these shall be the lines of the shadows in the beginning and end of the other hours But the Style must be so elevated from the Center of the Horologe above the Meridian line that the Angle which it maketh with it may be equal to the Latitude of the place or elevation of the Pole But it is more commodious to make some Triangle whose Angle at the Basis is equal to the Latitude of the place If the declination be made on Paper let the line be drawn from the Center which from the periphery may take an Arch equal to the Latitude of the place the Numeration being from the Meridian line and let the Triangle be cut out to be placed above the Meridian line so the shadow will shew the hours The making of this Scioterick is easie without a Globe Proposition XXIII To describe a Scioterick on a vertical Plain which may directly regard the East and West Aequinoctial A Scioterick what The making of this is perfected after the same Mode which we used in the Horizontal if that the Pole be not elevated according to the Latitude of the place but according to the Complement of it and then the Style also be elevated above the Meridian
found at the day taken and noted in the Ecliptick of the Globe Then let the Pole be Elevated for the Latitude of the Earth of the one place taken and let the Longitude of the day and the night or the stay of the Sun above or beneath the Horizon in that place at the assumed day be found by the sixth Proposition of this Chap. Then let the Pole be Elevated for the Latitude of the other place and let the Longitude of the day and night or stay of the Sun above or beneath the Horizon be found at the same assumed day Let this Longitude so found be compared with the other and the truth of this Proposition will be manifest So that the place more remote hath all the daies of one half year longer than the place more nigh On the contrary it will have all the daies of the other half year shorter Corollary What hath been shewed of all the daies of the year except the Aequinoctials the same is also of force in the quantity of the longest and shortest day And in this it is most observed and noted because here is the greatest difference between the Longitude of the night and day not so great in other daies of the year Therefore of the two places that which is more remote from the Aequator or more near to the Pole hath the longest day greater than the place more Vicine to the Aequator and the shortest day lesser Proposition VIII All places of the Earth scituated in one of the same Parallel have all the days of the year equal and therefore the same quantity of the longest day The Demonstration of this Proposition is easie by the Globe Let any Parallel be taken in the Globe and what places you please The equality of the daies according to their scituation in one of the same Parallel Let the Pole be Elevated for the Latitude of this Parallel and let any Parallel of the Sun be taken for any part of the year Out of the Degree let the Tropick of Cancer be taken for the longest day let one of the places taken be constituted under the Meridian that so it may possess the Vertex of the Horizon or that the Wooden Horizon may be the Horizon of the place Then let the Arch of the Tropick above the Horizon be noted or the two points of the same which are in the Horizon for the Arch in these denoteth the stay of the Sun above the Horizon of the place then let the second place be brought to the Meridian or Vertex that the Wooden Horizon may be the Horizon of it and let the Arch of the Tropick above the Horizon again be marked which if it be compared with the former we shall find that they are equal The same may be shewed also by hours on the Horary Circle Therefore the Sun remaineth an equal time above the Horizons of those places and therefore the daies shall be equal as also the nights Definitions From these aforesaid Propositions the Original of the division of the Earth into Climates is easily to be understood Observations concerning a Climate For a Climate is said to be one part of the Earth of those parts into which the Superficies scituated between the Aequator and the Pole is so cut by drawn Parallels that the longest day in the Parallel more remote from the Aequator exceedeth the longest day of the Parallel more near the Equator in a certain part of an hour or number of hours Viz. Half an hour in places scituated even to the Artick Circle in other places a whole hour or some hours and daies The begining of a Climate is called a Parrallel with which the Climate begineth and is more nigh the Aequator The end of a Climate is called a Parallel terminating the Climate The middle of a Climate is called a Parallel drawn almost through the middle Superficies of a Climate so that in that the longest day exceedeth the longest day of the begining of a Climate by a quarter of an hour or an half difference wherein the longest day of the end of a Climate exceedeth the longest day of the begining of a Climate A Parrallel space is said to be that which the middle Parrallel of a Climate comprehendeth with the begining or end of a Climate Proposition IX If more places of the Earth be taken from the Aequator towards the Pole whose distance from the Aequator equally augmenteth from one degree to 10 20 30 40 degrees The longest days in these places shall not be equally greater or not equally augment but they shall more augment in places more remote and where the place is more near to the Pole Touching the length of daies of Places taken from the Aequator towards the Pole To shew the Verity of this Proposition by the Globe let places be taken remote from the Aequator towards the Pole by an equal encrease of distance viz. for conveniency Parallels of 10 20 30 40 50 60 degrees of Latitude For these Parallels in the Globe let the Pole be Elevated to the Latitude of 10 degrees and the first degree of Cancer being brought to the Oriental Horizon and that being noted let the point of the Tropick be also noted which then is in the Occidental Horizon For the Arch of the Tropick then being above the Horizon sheweth the stay of the Sun above the Horizon of the place 10 degrees of Latitude The hours of this his stay may also be known by the Index and Horary Circle Then let the Pole be Elevated according to the Latitude of the second place 20 degrees and the first degree of Cancer being again brought to the Oriental Horizon let the point of the Tropick be noted in the Occidental for the Arch above the Horizon will again note the stay which also may be known by the Index and the Circle in the Hours The same may be used with places whose Latitude is 40 50 60 70 degrees and the like which being done let the Diurual hours of the Suns stay above the the Horizon or the Arch of the Tropick be compared and it will be manifest that the quantity of the longest day doth much more increase in places more remote than in the places more adjacent to the Aequator and therefore the encrease of the longest day doth more augment than the encrease of the distance of the places from the Aequator Note what hath been said and shewed concerning the longest day that is true of all the daies of one half of the year and is demonstrated after the same manner if instead of the Tropick of Cancer the Parallel of the place be taken And therefore although Generals must be delivered generally yet because the Doctrine of Climates especially requireth the Explication of the increase of the longest day therefore we do not observe in this Doctrine that Law 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Proposition X. If so many places or Parallels are so taken between the Aequator and
or Heaven which the Meridian line being found is easie to do by the Mariners Compass or the Magnetick Needle The Globe being thus placed at every moment of the day when the Sun shineth on the Globe may be seen the part of the Earth illuminated and the part not illuminated Those places which lie in the middle Semicircle of the part illuminated are those which will have the Meridies at that moment of time To those which are seated in the Oriental Semicircle dividing the illuminated part from the part not illuminated the Sun setteth but to those which are in the Occidental Semicircle separating the illuminated part from the part not illuminated the Sun riseth To find out the place of the Sun in the Ecliptick let the Needle or Spherical Gromon be moved hither and thither perpendicularly about the middle of the part illuminated until it maketh no shadow and let the point in the Globe be noted 〈◊〉 for this being brought to the Meridian here will shew the declination of the Ecliptick point in which the Sun is at the time of the Observation whence according to the condition of the time to wit Spring Summer Autumn or Winter the place of the Sun shall be known and thence the day of the year Also the place in the Globe unto which the Needle being affixed gave no shadow is that to which the Sun is vertical at that moment of time and the Parallel passing through this place will exhibit all the places in which the Sun will be vertical on that day Moreover to find the hour of the place in which the Globe is so placed or hung let that place be brought to the Meridian to which the Sun is vertical the Index to the 12th hour of the horary Circle and let the Globe be turned round until our place or that in which the Globe is seated do come to the Meridian the Index will shew the hour But because the Globe cannot be turned round when it is affixed by the Iron Style to the Horizontal plain therefore it will be convenient that the Quadrant be tied to the Pole or part of the Circle of the Periphery 113 â— â— for here the Arch being brought to the place of the Needle will shew the declination of the Sun from the Aequator whence the place of the Sun and the day of the year shall be found The same Arch will shew the degree in the Aequator from whence if that the degrees be numbred to the Brazen Meridian and these degrees be changed into hours or parts of hours Fifteen Degrees make an Hour you shall have the hour of the place If so be that the Sun be between the Occident and the Brazen Meridian that is of our place but if that it be between the East and our Meridian the hour found out must be subtracted from 12 and the remaining number will shew the hours from Midnight If that such a Brazen Arch be adjoyned to the Pole of the Globe as I have described 113 ½ degrees it may be bored through from the end even to 47 degrees that is from the departure of the Sun from the Aequator and a turning Plate be inserted in it which may bear the perpendicular Style and so there will neither be need of a Needle or of a Spherical Gnomon and the operation will be less obnoxious to errour Proposition II. The Terrestrial Globe being â—o placed as in the former Proposition is declared it will also shew when the Moon shineth to what People at any moment of time in which it is above our Horizon it is conspicuous to whom it ariseth to whom it setteth and to whom it is vertical These are all manifest from the preceding Proposition See Proposit 1. Proposition III. By how much the places of the Earth are remote from the Parallel of the Sun on any day by so much the Sun is elevated to a lesser Altitude in the same hours above their Horizon Let the places in the same Meridian be taken in the Globe for these do reckon all the same hours and that at once then let a Parallel be described for any assumed day and it will be manifest that any point of this Parallel is farther distant from the more remote places than from the places more near The Sun therefore being above the points of this Parallel will be farther distant from the Vertex of the remoter places than from the Vertex of those that are nearer and therefore he shall be less elevated over the Horizon of those places than of these Proposition IV. By how much the places of the Earth are more remote from the Aequator or more near the Pole by so much the more the parts of the Horizon are distant in which the Sun riseth on the day of the Solstice and the day of the Winter as also those in which he setteth The same is true concerning the Moon and all the Planets Take what places you please of a diverse distance from the Aequator and let the Pole be elevated for the Latitude of every one of them and let the points be noted in the Horizon in which the Tropicks of Capricorn and Cancer cut it A comparison being made the truth of the Proposition will appear this is also shewed the same way by how much the places are more remote from the Aequator by so much the more the Sun in his Aequinoctial rising is distant in the East on every day of the year The Astronomers term it the rising Amplitude Proposition V. Stars placed between the Parallel of any place lying without the Aequator and the Pole are less elevated above the Horizon of the places between this Parallel and the other Pole of those scituated there than above the Horizon of the places scituated between this Parallel and the nearer Pole Of the elevation of Stars c. The Parallel of any Star may be designed on the Terrestrial Globe or a point only noted for a Star and any place more remote from the Pole being assumed designeth the Parallel of the place Then taking another place scituated towards the other Pole the stay of the Star above the Horizon of both places may be found and the truth of the Proposition will be manifest Proposition VI. In places scituate in and near the Aequator the Sun and Stars directly ascend above the Horizon even to the Meridian and so descend again but in places scituated above the Aequator they obliquely ascend and descend and so much the more obliquely by how much the place is more remote from the Aequator Of the ascension and descension of the Sun and Stars Let any Parallel of the Sun be described on the Globe such as some already are delineated on the Globe viz. the Aequator the Tropicks and some Intermedial ones then let the Poles be placed in the very Horizon that it may be the Horizon of the places of the Aequator and it will be evident that the points of the
the Latitude of the place known and the distance of the unknown place being turned into degrees and the Angle comprehended from the Plaga given from these three given the opposite Angle to the distance must be sought for For this will exhibit the Longitude of the other place from the known place But on the Globe and Mariners Charts the place is thus found let the Pole be Elevated for the Latitude of the place given let the Quadrant be applyed to the Vertex and let the other extremity be applyed to the given Plaga of the Horizon Then the distance given being turned into degrees let it be reckoned on the Quadrant from the Vertex The term of the Numeration shall be the place sought for on the Globe But if that the Longitude be only sought for without the designation of the place that is if you are minded to resolve a Spherical Triangle by the Globe it will be done after this Mode We will give Examples in the 33 Chapter See Chap. 33. which is also to be observed in the following Chapters There also we will shew by one Example how such Problems may be resolved by the Planisphere Concerning all these also Tutors may instruct their Scholars from the Method of the Logarithms if that they be studious in these matters But Mariners use Calculation or the Plaine Sphere A Globe not commodious in a Ship For the use of a Globe is not so commodious in a Ship In Mariners Charts Let a Line be drawn from the given place for the given quarter and by the interval of the Compasses let it be taken on the Scale the distance of the places being opposited and one Foot being fixed on the place given let the other Foot be placed in the Line drawn for the Plaga or quarter This Point shall be the place sought for but yet not exact as we shall shew in the following Chapter The fourth Mode The distance of a place unknown being given from two places known to exhibit that and the known one in the Globe and Maps but to enquire its Longitude by Calculation The fourth Mode In the Globe Let one distance by the interval of the Compasses turned into degrees be taken on the Aequator and one Foot being fixed in the place from those given whose distance was not taken let an Arch be drawn on the Superficies of the Globe by the other Foot which hath the Chalk at its end After the same Mode a distance being taken from any other place let an Arch be described from this as from a Center on the Superficies the Point in which this Arch cutteth the former is the place demanded In Mariners Charts we must act after the same manner but yet the distances given must not be changed into degrees but must be taken on the opposite Scale But if the place be somewhat more remote from the place given an over great error may be committed by reason that the Charts do not perform this accurately The invention of Longitude by Calculation because it hath much difficulty as the Diagram requireth therefore I shall leave it to be taught by some Tutor and not describe it in words The fifth Mode Two places in the Earth being given and the Quarters in which some other unknown place is scituated at them to find out this third place in the Earth Maps and Globe and to enquire the Longitude of this place by Calculation The fifth Mode In the Globe Let one of the given places be brought to the Meridian and let the Pole be Elevated near its Latitude let the Quadrant be applyed to the Vertex and with the other end in which to wit at this noted place the third unknown place is put to lye and at the Margent of the Quadrant by a pointed Chalk let a small Periphery be drawn Then let the other given place be brought to the Meridian and the Pole Elevated near to its Latitude let the Quadrant be affixed to the Vertex and the other extremity to the given Plaga of the Horizon to wit in which the third unknown place is placed to lie at this same known place the Point in which the Margent of the Quadrant cutteth the Periphery before drawn with Chalk is the third place demanded On Maps It is thus done Let a Line be drawn from one given place for the given quarter of the three places after the same Mode let the Line of the quarter be drawn from the other given place The Point in which these two Lines mutually cut one another is the place demanded After the same Mode we should do on the Earth if that we would Act scientifically neither in Sciences do we value hinderances and impediments so that we may comprehend the Mode in our mind The Calculation in which our unknown Longitude of a place is found from these given we leave to the Instruction of a Tutor if that he hath apt and capable Scholars But more than enough hath been said concerning the invention of Longitude the ample use of which we have explained in the 2d Proposition Here should be added a Table of the Longitude and Latitude of the chief places of the Earth which the Author hath Collected and did here insert but being but short and having Maps of the several Kingdoms of the World in the other Part or Volumn to which the Latitudes and Longitudes are added they are thought convenient to be omitted here and referring the Reader to the particular Maps by which you may easily find the Latitude and Longitude of any place desired The fixed Stars as to their Declination and Ascension of great use in Geography and Navigation Moreover seeing that there is great use of Declination and Ascension of the fixed Stars both in Geography and Navigation I shall here add a Catalogue of the Stars of the first Magnitude with their Declination and direct Ascension at the Year 1650. For it is known from Astronomy that in progress of time a change is made in these by reason of the proper motion of the Stars above the Poles of the Ecliptick But in the use it is convenient to have such a Table of all the Stars because we have not alwaies a conveniency of using the same Stars But we only lay down these for Exercise and for the trying the proposed Problems in these This business belongeth to Astronomy but the use is notable both in other Sciences and also in Geography Astronomy sheweth how a Declination and direct Ascension may be found at every Year A TABLE of the DECLINATION And right Ascension of the Stars for the Year 1650. The Letter S sheweth the Northern Declination and the Letter A the Southern The Names of the Stars Declination Right Ascension Of the first Maginitude deg min. deg min. Oculus Tauri 15 46 S 64 0 Regulus or Cor Leonis 13 39 S 147 27 Cauda Leonis 16 32 S 172 59 Spica Virginis 9 17 A 196 44 Cor Scorpii 25
others given than to be used for the making of an intire Globe for it useth the distances of places Let the greatest Periphery or the Arch of the greatest Periphery be drawn through the Globe and in this from the given point let the Arch be taken as much as the distance of the other place is from the place first given the term of the Arch shall be other place Then if you will design any third place take by the interval of the Compass the distance of that third place from the other two even now designed and from these as from Centers let the Arches be described by these intervals of the Compass The point in which these Arches mutually cut one another is the point of the third place But as I have said that this Mode is not commodious for the intire designation of the Globe but when we will design any place in the Globe now made which is not yet in it and desire to do it from the only noted distance of that place from the two others which are found in the Globe because it is easy and we have not time by reason of Calculation to search the Longitude and Latitude of this third unknown place For thus we shall easily find the scituation of this point or place in the Globe and also the Longitude and Latitude then the Problem is this The distance of a place being given from two places that are found on the Globe to design the scituation of that place on the Globe whose distance is given of which in the following Chapter The third Mode the Vulgar one of Artificers The third Mode of making of Globes The third Mode of exhibiting and representing the Superficies and places of the Earth in the given Globe is that which Artificers use in the making of all Globes both Celestial and Terrestrial except those great ones of which I have now spoken which have nothing of compendiousness or commendation from the facility if that the places of the Earth be but only to be represented from one Superficies of the Globe but it is to be done on the Superficies of the Globes of the same Magnitude this practice hath great Prerogative before the other for the Mode is thus the Superficies of the Globe and the Earth is conceived to be divided into twelve parts or more if the Globe be to be made of a larger form through the Meridians drawn from Pole to Pole so that in any two Meridians the 12th part of a Superficies is included from Pole to Pole Then on a Plain let the like Figure be included in such a part of the 12 in two Arches which then in the Globe make the half Periphery of the Meridians And in many Meridians drawn through every degree of the Aequator and divided into portions and segments of the Parallels affordeth a kind of lettice work the portion of the Aequator is in the midst all the Meridians end in the Poles then c. e Meridian being taken for the first which the Tables of Lonâ—itude acknowledge let the degrees be noted from it in the Aequator the numbers being ascribed so that the degrees of Longitude of every place may â—e accounted Then in every one of these places representing the 12 parts of the Superficies of the Globe let the places be noted for the places of the Earth every one at his degrees of Longitude and Latitude which are extracted from the Table and the name is ascribed to the Table and the tracts of the Rivers and Bays drawn as also of the Lands these being thus described on Paper or Wood then make an incision and engrave according to that exemplar in Plates of Brass which then is fit for the Printing Press Which are afterwards applyed and joyned to the Superficies of the Globe so that its ends may touch the Axis or Poles of the Globe yet in many the Papers do not touch the Poles but are so made only to touch the Artick or Antarctick Circles and peculiar Papers are taken for the Polary Spaces For so they are more easily applyed especially in great ones so in the Superficies of this Globe all the places of the Earth are exhibited to which is then added a Brass Meridian and Horizon with a Foot Horary Circle and an Index The things worthy of note in this Mode There are two things in this description which require a more full explication all the rest I suppose to be plain and intelligible First after what Mode these 12 or 24 parts are to be described according to the Example of which the engraving in Brass must be made Secondly how plain Paper can be applyed to the Superficies of the Globe The first is thus donâ—â—ommodiously enough For Example let the 12 portion of the Hemisphere from the Pole to the Aequator be applyed to the Globe First from the known Diameter of the Globe let the quantity of the greatest Periphery be found out according to the proportion of Archimedes or the other proportion of the Periphery to the Diameter For Example let the Diameter of the Globe be two Foot and let the Longitude of the Foot in the noted Paper be divided into 10 digits and the 10 digits into 10 grains that there may be 100 parts in a Foot Let it be done so that as 7 is to 22 so 200 is to 628 4 7 parts or 6 28 200 Foot for the Periphery the fourth part of this that is the Quadrant of the Periphery shall be of 157 1 7 hundred or 1 57 10071 Feet and the 12th part of 52 19 21 hundreds or ½ a Foot and 2 hundreds and 19 21 of an hundred These being found let a long Line of 52 19 21 hundreds be drawn on the Paper from the ascribed Scale from the middle of this Line let a long perpendicular of 157 19 21 hundred be erected which shall be the Quadrant its extremity shall be the Pole and may be divided into degrees you have the Longitude of one degree if you divide 628 â— 7 by 360 Then let a Periphery be described from the Pole through the beginning of every degree or of every tenth they shall be Parallels in these Peripheries from both parts of the drawn perpendicular let that part be cut off by the Compass as much as is the 1 24 of the Periphery Now how great it is in the opposite Scale is known from the proportion of the Parallels to the Aequator which we have delivered in the end of the IV. Chapter See Chap. 4. So the points being signed in every Periphery and Arch you please a Line must be drawn through them and part of the Paper perminated by these Lines must be cut off For this being applyed to the Globe will possess 1 12 of the Hemisphere Now the application is easily performed viz. if that the portions be small for in these the distance between streight and Crooked is little discovered especially of the Earth when the Paper hath first
now this Problem is the same with that to find out the Meridian Line and the North and South quarters for these being known it is easy to know the rest First by the Stars viz. in the night the Bear or the Helice and Polary Star so called in the extremity of the tail of the Vrsa Minor of great same amongst the Ancients which shewed the North quarter whence all the rest are found for the face being turned to the North the East is at the right hand and the West on the left the Line of which quarters at Right Angles cutteth the Line of the North and South And these Cardinal quarters being found it is easy to find the intermedial quarters unto which purpose that there may be no need of a description they had a Circle made with the quarters whose Northern Line being placed above the Northern Line of any place the other quarters at one sight are discovered But in the day they sought out the quarter by the rising or setting of the Sun as we have shewed in the XXVIII Chapter See Chap. 28. 2. The other Method of the Antients for the knowing of quarters was the knowledge of the scituation or extension of the Shoars and one Promontory to the other For seeing the quarter of this extension was known to them either from the Maps or from Observation and Experience they might in Navigation by seeing them know the other quarters For one quarter being known all the rest are known therefore the Ancients did not far depart from the Coasts viz. that they might know the quarter by the benefit of the known quarter of the extension of Shoars For they could not always use the Method of the Stars and the rising and setting of the Sun 3. The third Method of the Ancients of the knowledge of the quarters was the observed course of the Ship For going from any place and guiding the Ship to the known quarter they were able from the mutation of the course of the Ship to know the quarters 4. Hence it is manifest that the chief cause of the dangerous and imperfect Navigation of the Ancients was the ignorance of a Method by which every where in the middle of the vast Ocean they might know the quarters and so that quarter unto which the Ship was to be steered For as I have said the Method by the Stars and the rising and setting Sun cannot be applied on all days and on the hours of every day for the mark from the scituation of the Shoars faileth in the mid Seas in the night neither is it safe enough in the day time The third Method from the observed course of the Ship hath not place when the Ship is tossed by boysterous winds and tempests from one quarter to another And in this casually lyeth the chief difficulty This I thought fit to admonish concerning the Modes of the Ancients for the finding out the Meridian Line and the North and South by reason that the imperfection of these was the cause of the dangerous and small Navigation of the Ancients seeing that they were never able to commit themselves to the vast Ocean and therefore never knew those Regions between which the Ocean is interposed of which the chief is all America never yet fully known But at this day the Method of knowing the quarters in all places and of finding out the Line of the North and South is facile by the benefit of the admirable propriety which the Loadstone and all Iron touched by it hath been found to have Viz. that all Magneticks not hindred by others in any place direct their points almost to the same quarters For there are two opposite points in the Loadstone whereof one always and in all places turneth it self to the North or the adjacent quarter the other to the South and so also the other points of the Magnes respect the other quarters viz. every point its particular quarter but all of them are not considered but only those two points which as I have said do convert themselves to the North and South which are termed the Poles of the Magnes one Northern the other Southern And the same virtue much to admiration is communicated to the Needle but by an inverted and contrary operation of nature For the end of the Lamine or Needle which is touched at the North Pole of the Magnes doth not convert it self to the North but to the South and that end which is rubbed at the South Pole of the Loadstone turneth not to the South but to the North. These points of the Needle are also termed the Poles The virtue of the Loadstone Although therefore the Loadstone and the Iron touched by it have very many notable properties yet all may be referred to two species or heads one is that virtue which doth extract the Iron the other by which in every place it directeth the two points of its Superficies to the North and South The former faculty the Ancients were not ignorant of but only this latter Seeing therefore the Magnes hath this property therefore by its help it is easy to find in any part of the Earth or Sea where the North or South is whence all the other quarters are soon known For if those points of the North and South be noted in any Loadstone or the North and South Pole and we have this Magnes in the Ship where we are in the Sea when we desire to know the quarters the Loadstone being hung by a Cord that it may easily move it self will so direct its Poles to the quarter of the North and South that it will shew the quarters demanded But the Magnetick Needle is more easy for use whose end is touched at the South Pole of the Magnes For if that this Needle be placed in the middle upon a sharp perpendicular pin so that it can freely turn round the Needle resting will shew by one of its ends the North quarter and by the other the South From what hath been said it is easy to make a Nautical Instrument Proposition II. To make a Mariners Compass Of the making the Mariners Compass Let the described Circle on any Paper be divided into 32 Quarters or degrees and let one of these deg being taken for the North Quarter be ascribed with these appellations Viz. with a peculiar Sign the Flower de Luce and the found out points for the other Quarters viz. South East West North-East North-West as we have propounded them in the Diagram in the XX Chapter Mariners term this Chart the Rose Then let the Magnetick Needle be so affixed beneath the Chart that the middle of the Needle may be beneath its Center and the North Pole of the Needle may be subjected to the Line of the Paper unto which we ascribe the Northern Quarter Moreover the Paper being so made with the Needle lying under let it be put upon the pointed pin that it may have a free Circumrotation So the Index of the
principal Xecque that is a Chief which conducts and commands them they living almost in the same manner as the 12 Tribes of Israel did in the Desarts They preserve a good Intelligence amongst themselves their chief design being only upon Strangers They assault likewise the Caravans if they think themselves able enough to master them or snatch any thing from them Their Horses commonly are little lean and sparing Feeders yet couragious swift and of great labour They are so skilful in managing them that they command them as they please and themselves are so active that at full speed they will shoot an Arrow within the breadth of a Shilling take from the ground those Arrows they have shot and avoid an Arrow flying directly towards them nor do they manage less skilfully the Sling either in charging retiring or flying The first rise of Mahometism Mahomet came not into the World till about the year 570 after Christ and began not to publish and shew abroad his Doctrine till a little after the year 600 a Doctrine intermixed with Christianity Judaism and Paganism that he might draw both the one and the other and which established its principal end in Delights carnal and sensual Pleasures whereto the Oriental People were very much inclined and withal he found the means to make use of Arms for the establishment of this Doctrine his Califs or Successors in a short time carried their Government and Religion into the best parts of Asia and Africa and into some places of Europe It s People are almost all Mahometans There are some Greek Christians towards the Mounts of Sinai and Horeb likewise towards the Red Sea and in the Desarts of Arabia the Stony and Arabia the Desart Arabia the Happy is unhappy in having the fewest yet the Portugals hold Mascates Calasates and some places about it which are Catholicks PERSIA or the Empire of the SOPHY of PERSIA with its several Provinces as they lie Towards the CASPIAN Sea or Sea of BACCU and SALA which makes the Northern part of PERSIA and are those of Servan Tauris Sammachi Servan Ardevil Serga Bacca â—â—kâ—era Gilan Rast Gaxhar Mazandaran Layon Mosun Gilan Cassabi Gadiour Dilemon Allamoed Dilemon Thalekan Tabarestan Aâ—â—erâ—â—ad Zarâ—â—â—â—â— Magâ—â—â—â—n Gorgian Gorgian Obâ—â—oen Darâ—egan Semnan Rhoemus Bestan Bâ—yâ—â— Zabrawar Thous Masâ—ndn Feraway In the MIDDLE to wit those of Churdistan Naksivan Merend Choy Maraga Salmas Ourmaya Cormaba Ayrack or Yerack-Agemi Hispahan Casbin Saltania Dankane Hamadan Hrey Sauwa Kom or Com Kargh Cassian Yesd Chorasan Thabs Gilack Kayem Thon Zuzan Mexat Nichabour Zarchas Firabad Maruwe Bonregian Balch Herat. Sablestan Zarang Bost Necbesaet Gisna-Cassaby Tocharestan Thaalan Candahar Candahar Patanes Grees Bach Balch Towards the South and washed by the ARABIAN or INDIAN Ocean and by the Gulph of BALSORA and ORMUS and are those of Chusistan Souster Askar Moukeraâ— Ardgan Hawecz Ramhormoz Siapour Saurac Fars Chiraef Aftackar Lar Darabegred Stahabonon Gombroun Kherman Cherman Girost Zirgian Mocheston Guadel Nahyan Patanis Sigistan Sistan Mackeran Mackeran Basir Together with several ISLES as they lie in the Gulph of BALSORA and nigh unto PERSIA the chief among which are Ormus Ormus Queixome Pulor Coyar Ficor Lar. Mulugan Garge PERSIA THe Kingdom or Empire of the Sophy of the PERSIANS is one of the most famous and greatest of all Asia it extends it self from the Tigris and Euphrates on the West almost to the River Indus on the East and from the Gulph of Persia and the Arabian and Indian Sea which bounds it on the South unto the River Gehon and to the Caspian Sea now the Sea of Baccu or Tabarestan which are its Northern limits The extent bounds scituation c. of Persia so containing about 600 Leagues of length and 500 of breadth being seated under the third fourth fifth and sixth Climats Nevertheless this is but a part of the ancient Empire of the Persians for the Assyrians having ordinarily held in Asia all that which both Turk and Persian at present possess and that Monarchy having begun under Ninus and lasted under thirty and odd Kings 13 or 1400 years ending in Sardanapalus divided itself into that of the Medes and Babylonians who continued it little less than 300 years afterwards the Persians made themselves Masters of it and these during 200 and odd years which they Reigned remitted to it the best part of what the Medes and Babylonians had possessed But when they would have passed into Europe and have seized on Greece the Macedonians and Greeks leagued themselves together The Persian Empire formerly much larger than now it is and naming Alexander King of Macedon their Chief descended into Asia several times defeated Darius ruined the Empire of the Persians and gave a beginning to that of the Macedonians Alexander the Great held this Empire but few years and dying it was divided among many of his Captains who took in the end the title of Kings and waged War against each other till the Romans seized the Western and the Parthians the Oriental part of that Monarchy these Parthians freed themselves from the Rule of the Macedonians 250 years before the Birth of Jesus Christ and Reigned near 500 years Artaxerxes restored the Persians 228 years after Christs Nativity The Caliphs of Bagdat became Masters about the year 650. The Tartars in 1257 or 58. The Turcomans in 1478. Xa or Xecque Ismael-sophy re-established the Persians a little after the year 1500 and though they possess only the Oriental part of the ancient Empire of the Persians yet it is still very great and powerful The several Parts or Regions of Persia And we find at present under it all that the Ancients knew under the names of Media Hircania Margiana Assyria in part Parthia Aria Paraponisa Chaldea or Babylonia in part Susiana Persia Caramania Drangiana Arachosia and Gedrosia all these Regions taken apart being great fair rich and populous To the Right Worshipfull Sr William Courteney of Powderham Castle in Devonshire Bart. This Mapp is Hu-mbly didicated by RB A MAPP OF THE EMPIRE OF THE SOPHIE OF PERSIA WITH ITS SEUERALL PROUINCES Designed by Moncr. Sanson Geographer to the French King Province of Gilan and its chief places c. The Province of GILAN or GVEYLAN contains five Governments of which the chief Cities are Rast Gaxhar Layon Gilan Mosun and Gadiour besides about 30 fair and rich Cities Mazandaran which some separate from others joyn to Gilan hath in its Government 25 Cities and in the City of Mazandaran about 50000 Souls All these quarters would have revolted in 1594. but Xa Abbas soon brought them to their duty and chastised them for their offence Province of Dilemon The Province of DILEMON hath its Metropolis of the same name then Allamoed Gowar and Thalekan In the description that those of the Country give us of these places Allamoed seems to answer to Dilemon Province of Tabarestan The Province or TABARESTAN extends more than 60 Leagues on the Coast